Rydberg-Klein-Rees Research Articles

The 5 1Σ+g and 6 1Σ+g States of 39K2 Studied by Optical-Optical Double Resonance Spectroscopy

The molecular constants of the previously unobserved 5 and 6 1Σ+g states of K2 are determined and the potential curves are constructed using the Rydberg-Klein-Rees (RKR) method. The absolute vibrational numbering of the 5 1Σ+g state is obtained by comparing the intensities of resolved fluorescence spectra with calculated Franck-Condon (FC) factors.

Optical-Optical Double-Resonance Excitation Spectra of the (6 d) 1Δ g and (7 d) 1Δ g Rydberg States in Na 2

The levels with ν ≤ 14, 27 ≤ J ≤ 57 in the (6 d) 1Δ g and (7 d) 1Δ g Rydberg states of Na 2 have been observed using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in the B 1Π u state are identified by numerical calculations with the molecular constants for B 1Π u ← X 1Σ + g transitions and confirmed by the complementary A 1Σ + u ← X 1Σ + g polarization spectra. Absolute vibrational numberings of the (6 d) 1Δ g and (7 d) 1Δ g states are determined by comparing the observed OODR excitation intensities of transitions 1Δ g ← B 1Π u with that of the simulated Franck-Condon factors. The Dunham coefficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6 d) 1Δ g and (7 d) 1Δ g states are reported.

Analysis of the A2Πi ~ X2Σ+ perturbations of the AlO radical

The A2Πi ~ X2Σ+ perturbations of the AlO radical were analyzed in the mixed levels of (νA, νX) = (0, 5), (1, 6), (2, 7), (3, 8), and (4, 9) by a simultaneous analysis of the reported D2Σ+–A2Πi transition wave numbers and the A2Πi–X2Σ+ energy level differences, the latter being evaluated by taking the differences of the reported wave numbers of the C2Πr–X2Σ+ and C2Πr–A2Πi transitions. The molecular constants for A2Πi, ν = 0–4; D2Σ+, ν = 0–5; and X2Σ+, ν = 8 and 9, and the perturbation constants were determined. The Rydberg–Klein–Rees (RKR) potentials of the A2Πi and D2Σ+ states were obtained using these molecular constants. The spin-orbit constants, Aν, for A2Πi are discussed in terms of the electronic structure of the A2Πi state.

Optical-Optical Double Resonance Spectroscopy of the 2 1Π g State of Na 2 Using an Ultrasensitive Ionization Detector

Using optical-optical double resonance and an ultrasensitive ionization detector, we have been able to extensively study a wide range of internuclear distances for the 2 1Π g state of Na 2. A total of 80 vibrational levels (0 ≤ v ≤ 43 are from previous work using filter-PMT detection) which covered more than 99.9% of the well depth were observed in this state. The Rydberg-Klein-Rees (RKR) potential energy curve was constructed with a maximum outer turning point R 79+ = 18.08 Å. The potential curve at long range, where it can be described in terms of C n coefficients, is also discussed.

Optical-Optical Double Resonance Spectroscopy of the 6 1Σ +g Shelf State of Na 2 Using an Ultrasensitive Ionization Detector

The Na 2 6 1Σ + g state has been observed from v = 0 to v = 39 by using optical-optical double resonance spectroscopy and an ultrasensitive ionization detector. The molecular constants and the Rydberg-Klein-Rees (RKR) potential energy curve are presented in this paper. Eigenvalues calculated from the ab initio potential [S. Magnier et al., J. Chem. Phys. 98, 7113-7125 (1993)] are also discussed.

Optical-Optical Double-Resonance Excitation Spectra of the (6d) 1 Π g , (7d) 1 Π g High-Lying Rydberg States in Na 2

Two 1Πg states of Na2 for v ≤ 13 have been observed by using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in B1Πu state are identified by the numerical calculations with the molecular constants for B1Πu ← X1Σg+ transitions and confirmed by the complementary A1Σu+ ← X1Σg+ polarization spectra. Absolute vibrational numberings of the (6d)1Πg and (7d)1Πg states are determined by comparing the experimental OODR excitation intensities with the simulated Franck-Condon factors. The Dunham coefficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6d)1Πg, (7d)1Πg states are reported.

Optical–optical double resonance spectroscopy of the 4 1Σ+g ‘‘shelf’’ state of Na2 using an ultrasensitive ionization detector

The 4 1Σ+g ‘‘shelf’’ state of Na2 was extensively investigated using optical–optical double resonance spectroscopy and an ultrasensitive ionization detector. A total of 179 vibrational levels-(0≤v≤127 are from previous work by using filter-photomultiplier tube fluorescence detection) were observed in this state, which covered more than 99.8% of the well depth. The Rydberg–Klein–Rees (RKR) potential energy curve was constructed with maximum outer turning point R178+= 17.60 Å. The comparison of the long range portion of the RKR potential energy curve and the potential curve calculated from V(R)=ΣnCn/Rn is discussed. Avoided crossings around the shelf with the 3 1Σ+g state and near dissociation with the 5 1Σ+g state are also discussed.

The 3 1Σ+g ‘‘shelf’’ state of Na2

The 3 1Σ+g state of Na2 has been extensively studied using an optical–optical double resonance technique and a shielded cylindrical space-charge-limited ionization detector. A wide range of vibrational quantum numbers 0≤v≤141 was observed which covered over 99.9% of the potential well depth. A ‘‘shelf’’ on the potential energy curve was found near v=23. A hybrid potential was constructed based on the Rydberg–Klein–Rees (RKR) potential curve and a local inverse perturbation approach (IPA) for the shelf region. For this potential, there is a shallow second local minimum ∼5 cm−1 in depth at the shelf region. The long range energy also compares well with long range theory.

Optical-Optical Double-Resonance Excitation Spectra of the (8d)1Δg High-Lying Rydberg State in Na2

The levels with v from 1 to 9 in the (8d)1Δg state of Na2 have been observed by means of optical-optical double-resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in the B1Πu state are justified by numerical calculations with the molecular constants by Kusch and Hessel (J. Chem. Phys.68, 2591-2607 (1978)) for B1Πu ← X1Σ+g transitions and confirmed by the complementary experiments for polarization spectra of A1Σ+g ← X1Σ+g transitions. The Dunham coefficients and the Rydberg-Klein-Rees (RKR) potential energy curve of the (8d)1Δg state are determined.

Construction of bound-state potential energy curves of diatomic molecules from vibration-rotational spectroscopic data

By means of a purely quantum mechanical method we construct accurate analytic adiabatic potential energy curves for diatomic molecules from vibration-rotational transition frequencies. Our potential energy functions for two sample molecules, CO and HCl, are in better agreement with available Rydberg-Klein-Rees (RKR) turning points and reproduce the experimental data more accurately than corresponding curves obtained by other authors. The perturbation series for the calculated line positions in terms of the small parameter 2B e/ω e, where B e, and ω e are the rotational and vibrational spectroscopic constants, respectively, exhibits better convergence properties when applied to our potential energy functions.

Predissociation lifetimes of vibrational levels of the excited 1B1 (K a′=0) electronic states of Cd⋅H2 and Cd⋅D2 complexes

The experimental rates of predissociation of vibrational levels of the 1B1 (Ka′=0) excited states of the Cd⋅H2 and Cd⋅D2 complexes are shown to be consistent with both semiclassical and quantum-mechanical pseudodiatomic theoretical treatments of the process. The 1B1 pseudodiatomic potential was constructed by fitting an analytical function to the experimentally estimated Rydberg–Klein–Rees (RKR) inner and outer turning points. The potential of the repulsive 3A1 state was estimated by fitting an exponential function to the ab initio points of Boatz, Gutowski, and Simons, then adjusting the exponential parameter slightly to maximize overall agreement with the observed Cd⋅H2 and Cd⋅D2 predissociation lifetimes. The best-fit repulsive curves for both the semiclassical and quantum-mechanism calculations result in slightly ‘‘outer-wall’’ 1B1/3A1 crossings at only 84 and 76 cm−1, respectively, above the 1B1 potential minimum. The 1B1/3A1 coupling matrix elements derived from both treatments were ∼150–160 cm−1, much smaller than the 404 cm−1 expected if the spin–orbit interaction were unchanged from that of the asymptotic Cd(5s5p) states. It is suggested that the apparent reduction in the coupling strength could be due to the marked change in the nature of the Cd 5pσ orbital due to the strong repulsive interaction with H2 in the 3A1 state and to the neglect of the anisotropy of the 1B1/3A1 triatomic potential surface crossing.

Rotational-RKR inversion of intermolecular stretching potentials: Extension to linear hydrogen bonded complexes

A Rydberg–Klein–Rees (RKR)-based method is described which determines effective 1D intermolecular stretching potentials for polyatomic linear complexes from high precision rotational data alone. This extends the ‘‘rotational RKR’’ inversion method from pseudodiatomic van der Waals clusters with only two nonhydrogenic atoms to much larger complexes with several heavy atoms. Sample inversion of rotational eigenvalues generated from a model 1D potential reproduces the model potential to ≲0.13 cm−1 accuracy and correctly predicts harmonic frequencies, force constants, and dissociation energies to ≲0.1%. In contrast, the commonly used ‘‘pseudodiatomic’’ approximation lead to quite significant (10%–20%) errors, even for exact model potentials for which these approximations were developed. The method is further tested on high resolution near IR spectroscopic data of 14N14N–HF, which determines the vibrationally averaged hydrogen bond stretching potential from 3.39≲Rcm≲3.85 Å. The RKR data yield a hydrogen bond length of RN–H=2.106 Å (2.079 Å) and predict a van der Waals stretching frequency of 86.9 cm−1 (90.7 cm−1) for vHF=0 (vHF=1). RKR fits that incorporate electrostatic models of long-range behavior also permit estimates of the hydrogen bond dissociation energies and vibrational red shift for the vHF=0 and vHF=1 states, respectively. The range of D0 values agree reasonably well with previous ab initio calculations, and the difference in D0 values between vHF=0 and 1 is in good agreement with the experimentally observed red shift.

Inversion of experimental data and ab initio studies of a pseudo-atom–diatom model for the vibrational dynamics of HCN–HF

Spectroscopic data was inverted to generate simplified atom–diatom intermolecular potentials for the hydrogen bonded dimer HCN–HF. Both the HF ν1=0 and ν1=1 adiabatic surfaces of this complex involving the hydrogen bond stretch (ν4) and the high frequency HF bend (ν6) degrees of freedom were considered. Adiabatic separation of angular and radial degrees of freedom allowed a modified vibrational Rydberg–Klein–Rees (RKR) inversion to give effective radial potentials for each bending state. The final potential at a sequence of intermolecular separations was obtained by requiring agreement between the eigenvalues of the angular Hamiltonian and the effective radial potentials which were obtained from the RKR inversion. Potentials obtained from the inversion procedure were tested by a variational calculation with a basis set that consisted of products of preoptimized radial and angular eigenfunctions. Transition frequencies included in the inversion procedure were reproduced to better than 1 cm−1, respective rotational constants were predicted within 0.15% of the experimental value and predicted intensities were in qualitative agreement with experimental results. Ab initio potentials were also calculated using second order Mo/ller–Plesset perturbation theory to treat electron correlation effects and with a triple-zeta-valence basis set plus two sets of polarization functions. The energies were computed at geometries where the potential had been determined by the inversion procedure. A total of 264 geometries were considered. A correction for basis set superposition errors led to good agreement between ab initio and experimental values of the well depth. We calculated the bound states of the ab initio surfaces assuming the adiabatic separation of the ν1 mode from the ν4 and the ν6 modes. The transition frequencies calculated from the ab initio surface differed from the experimental energies by less than 20 cm−1 even for highly excited overtones. Both the potentials obtained from the inversion procedure and from the ab initio calculations were modified to predict the spectrum of HCN–DF.

The study of the 39K 2 Rydberg 1Δ g states by CW optical-optical double-resonance spectroscopy

Three intermediate-lying Rydberg 1Δ g states of 39K 2 were studied by CW optical-optical double-resonance (OODR) spectroscopy. The absolute vibrational numbering, the Dunham coefficients, the Rydberg-Klein-Rees (RKR) potential curves, and the Franck-Condon factors (FCF) of three ( nd) 1Δ g - B 1Π u systems are given. The variation with the principal quantum number n of the contribution of the ndδ g Rydberg electron to the binding energy is discussed. In addition, five observed successive ( nd) 1Δ g states included in this work ( n = 8, 9, and 10) and the work of Wang et al. ( J. Chem. Phys., in press) ( n = 6 and 7) are assigned absolute electronic state numbering based on the molecular building-up principle. Furthermore, the dissociation limits, the dissociation energies, and the quantum defects of those ( nd) 1Δ g states are compared with respect to the asymptotic assignments made by Broyer et al. ( Chem. Phys. Lett. 99, 206–212, 1983) and by Kowalczyk et al. ( Z. Phys. D. 13, 231–240, 1989); our work supports the assignment of Broyer et al.

Emission spectrum of the CN(B 2Σ+–X 2Σ+) tail band system: B 2Σ+∼4Π perturbations in the v B=9, 12, and 17 levels

The CN(B 2Σ+–X 2Σ+) tail band system was observed in the reaction of argon metastable atoms with BrCN. The observed transitions in the 17-14 and 17-16 bands were analyzed in terms of the B 2Σ+,v=17∼A 2Πinv,v=34 and 4Π,v=p+11 perturbations, and the molecular constants for these levels and the interaction constants were determined. Intensity anomalies were also observed in the 9-8, 9-9, and 12-12 bands. The quantum numbers of the total angular momentum, J, of the perturbed rotational levels of B 2Σ+ were assigned as (vB,N;J)=(9,56;55.5) and (12,10;10.5). The vibrational quantum number was determined as p=0, and the crossing spin sublevels at the anomalies of vB=9 and 12 were determined as 4Π5/2 and 4Π1/2 by examination of the electronic part of the B 2Σ+∼4Π perturbation constant, HSOel, for the (vB,vΠ)=(14,6) and (17,11) perturbations estimated by use of the Rydberg–Klein–Rees (RKR) potentials for B 2Σ+ and 4Π.

A reexamination of the Rydberg–Klein–Rees potential of the a 3Σ+u state of Na2

The ∼0.1 Å error in the inner wall of the experimental Rydberg–Klein–Rees (RKR) potential for the Na2 a 3Σ+u state [L. Li, S. F. Rice, and R. W. Field, J. Chem. Phys. 82, 1178 (1985)], detected by Jenč and Brandt using the reduced potential curve (RPC) method [F. Jenč and B. A. Brandt, J. Chem. Phys. 91, 3287 (1989)], was due to neglect of centrifugal distortion effects and not due to a fundamental flaw in the LeRoy–Bernstein near-dissociation expansion (NDE) G(v) and B(v) fitting expressions used to generate it. The NDE expressions, in fact, are preferable to the more traditional Dunham expansions of B(v) and G(v) for the fitting of sparse data sets. We have refined the previously published RKR curve to include centrifugal distortion effects without including additional data. The results are in excellent agreement with theoretical predictions, and are probably accurate to ±0.01 Å up to energies within 5 cm−1 of dissociation. The principal constants are Te+Y00=5848.48(22) cm−1, ωe=24.15(2) cm−1, Be=0.0562(1) cm−1, re=5.011(9) Å, and De=175.76(35) cm−1.

Potential model for diatomic molecules including the united-atom limit and its use in a multiproperty fit for argon

The extended Hartree–Fock approximate correlation energy potential model recently reported for diatomics has been improved to account for the Coulombic behaviour at the collapsed diatomic limit for vanishingly small interatomic separations, R→ 0. Also discussed is how to impose the appropriate inverse exponential dependence on R into the extended Hartree–Fock energy contribution as R→∞. Test results are presented for the ground states of 13 chemically stable diatomics and the Ar2 van der Waals molecule. For Ar2, the potential-energy function is obtained from a multiproperty fit including spectroscopic, scattering, and second virial coefficient data. For the remaining diatomics, the calibration procedure uses only spectroscopic Rydberg–Klein–Rees (RKR) data. The new Ar2 potential is then used to calculate the thermophysical properties of gaseous argon over the temperature range 102⩽T/K⩽ 105. In all cases, the potential-energy function of the present work has been found to be very accurate.

The Li2 C 1Πu state studied by a single-frequency ultraviolet laser

A newly constructed single-frequency, autoscan laser spectrometer operating in the ultraviolet in combination with a collimated molecular beam has been used to obtain a high resolution fluorescence excitation spectrum in the region 30 850–31 400 cm−1. Eight hundred and seventy five rotational lines of the 7Li2 C 1Πu(v′=2–8)–X 1Σ+g and 6Li7Li C 1Π(v′=2–4)–X 1Σ+ transitions are assigned. The molecular constants of the C 1Πu state are determined and the potential curve is constructed using the Rydberg–Klein–Rees (RKR) method. By comparing the calculated Franck–Condon factors with the line intensities of the dispersed fluorescence spectrum, we determine the dependence of the electric dipole transition moment on the internuclear distance.

Near infrared two-photon laser spectroscopy of the 2 1Σ+g state of 7Li2

The results of a nonresonant near infrared two-photon laser spectroscopic study of the 2 1Σ+g state of 7Li2 are presented. Over 1000 rotationaly resolved 2 1Σ+g←X 1Σ+g transitions spanning 2300 cm−1 of the 2 1Σ+g potential well have been assigned and analyzed. Data from the v′=1 to v′=21 vibrational levels are used to obtain 2 1Σ+g state Dunham molecular constants as well as band-by-band constants. These data are also used to construct a Rydberg–Klein–Rees (RKR) potential which corresponds to 89% of the potential well depth. The results for the lower v′ levels are in agreement with the previously determined molecular constants for v′=0 to v′=16 [J. Mol. Spectrosc. 116, 271 (1986)]. For the higher v′ levels they reveal the perturbations from the 1 1Πg state. Comparisons with the results of ab initio calculations are made. In the 2 1Σ+g←X 1Σ+g nonresonant two-photon excitation only Q-branch transitions are observed with plane polarized radiation.

Optical–optical double resonance spectroscopy of Cl2: First observation and analysis of the 0−g(3P1) ion-pair state and the lower-lying B′ 3Π(0−u) valence state

The perturbation facilitated optical–optical double resonance technique allows access to the 0−g(3P1) ion-pair state through the A 3Π(1u) v=9 intermediate state where the A 3Π(1u) ∼B′ 3Π(0−u) interaction occurs: 0−g(3P1) –{A 3Π(1u) ∼B′ 3Π(0−u) }–X 1Σ+g. Molecular constants of the 0−g(3P1) state are derived from 197 transitions in the 0≤v′≤15 and 9≤J′≤47 range, and a Rydberg–Klein–Rees (RKR) potential based on these constants is given. The dispersed fluorescence spectra of the 0−g(3P1) –B′ 3Π(0−u) system are used to establish the absolute vibrational numbering of the 0−g(3P1) state, and also to characterize the new B′ 3Π(0−u) state in view of the Franck–Condon factor consideration.